薄壁结构响应特性有限元数值模拟和疲劳寿命预测方法研究
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摘要
薄壁结构由于质量轻、承载性能优良,被广泛用于航空航天、船舶、汽车、压力容器等领域。此类结构的应力和应变受几何形状、边界条件等因素影响较大,除特殊情况外难以获得解析解,因此薄壁结构的基础理论和模拟方法一直是研究的热点。本文针对薄壁结构响应特性数值模拟、稳定性分析和疲劳寿命预测研究中存在的问题,进行了如下内容的研究:
1.薄壁结构响应特性有限元模拟及误差修正方法研究
基于薄壁结构的控制方程和有限元离散原理,系统研究了包含倒角、凸台、孔洞等特征的曲面薄壁结构的有限元离散特点和建模方法。同时基于离散过程的理论推导,研究了有限尺寸曲面薄壁结构的离散误差产生机理和计算应力的修正方法。以探针为对象,分析了曲面薄壁结构的屈曲载荷随几何尺寸和外形的变化规律,为结构稳定性分析和优化奠定了基础。
2.薄壁结构基础振动数值计算方法研究
基于连续体基础振动原理和有限元实现过程,建立了求解薄壁结构简谐基础振动和冲击问题的静力等效载荷法。通过施加静力等效节点载荷将简谐基础振动问题转化为基础固定的简谐响应问题,进而获得结构响应的幅值和时间历程,克服了现有方法的不足。
3.薄壁结构疲劳裂纹形成寿命预测及结果显示方法研究
基于疲劳累积损伤理论,建立了准静态和动态载荷作用下薄壁结构疲劳裂纹形成寿命的预测方法和有限元模拟及显示流程。同时以探针为对象,基于四点雨流计数法和双线性累积损伤准则,通过自编程序实现了薄壁结构疲劳寿命的自动预测和结果的图形化显示。
4.薄壁结构疲劳裂纹扩展寿命理论模型和预测方法研究
通过现有疲劳裂纹扩展速率影响因素特点和试验数据规律的研究,提出了描述试样厚度、循环应力比和材料参数等对疲劳裂纹扩展速率影响的综合影响系数模型。通过与Newman、Huang和Codrington模型对裂纹张开应力和有效应力强度因子范围比预测结果的对比,验证了模型的有效性。基于综合影响系数模型和钝化复锐理论开发了常幅和变幅载荷下疲劳裂纹扩展的通用模型,并通过试验数据和现有模型的预测结果验证了通用模型的有效性。
5.薄壁结构疲劳裂纹扩展过程数值模拟方法研究
基于第4部分的理论模型,采用扩展有限元和水平集法建立了常幅和变幅载荷下疲劳裂纹扩展过程的扩展有限元模拟流程和矩阵更新算法,并通过现有试验数据验证了理论模型、扩展有限元模拟流程和求解算法的有效性。
6.基于ANSYS的薄壁结构数值仿真和疲劳寿命预测专用软件开发
基于第1~5部分的研究成果,并以探针应用需求出发,开发了薄壁结构响应特性专用仿真和疲劳寿命预测软件。
本论文取得的主要创新成果如下:
1.提出了求解连续体简谐基础振动和冲击问题的静力等效载荷法该方法避免了瞬态计算方法中存在刚体位移、算法稳定性、模型规模等限制,以及反映谱法存在振形峰值组合规则的限制,可用于求解单点和多点非正弦(余弦)基础振动、冲击和瞬态响应等问题。
2.建立了反映材料特性、试样尺寸、载荷特征等参数对疲劳裂纹扩展速率影响的综合影响系数模型
该模型显式反映了材料特性、试样尺寸、循环应力比等因素对裂纹张开比和
有效应力强度因子范围比及疲劳裂纹扩展速率的影响。通过代入试样参数、试验条件和材料参数可预估结构和试样的疲劳特性,可为试验设计、试样选型和实际应用提供指导。
3.提出了常幅和变幅载荷下结构疲劳裂纹扩展过程的通用模型
该模型能有效且定量描述单峰过载、单峰低载、序列加载和谱载荷等产生的延迟和加速效应,具有明确的断裂力学的物理含义,适用于描述各种韧性材料、不同加载条件和不同试样类型的疲劳裂纹扩展过程。
4.建立了结构疲劳裂纹扩展过程的扩展有限元模拟流程和平衡方程更新算法该流程能有效模拟实际结构的疲劳裂纹扩展过程,同时通过水平集函数将模型分割为更新和非更新区域,疲劳裂纹扩展过程中仅需对更新区域的数据进行计算和集成,大大提高了求解效率。
Thin-walled structures are widely used in aeronautics, watercrafts, automobiles, vessels and so on because of its light weight and good load-carring property. But the theoretical stress and strain results of these structures can be hardly derived due to the influence of geometrical shape, boundary conditions and so on. Hence, the basic theory and numcerical simulation methods of these structures have been the research focus for decades. In the dissertation, the following topics are studied based on the problems existing in numerical simulation, stability analysis and fatigue life prediction:
1. Research on the finite element modeling method and error correction method of the response characteristics of thin-walled structures
The modeling method and discrete characteristics of curved thin-walled structures with chamfers, bosses, holes and so on are studied systematically based on its governing equations and the discrete principles of finite element method (FEM) at first. Then, the error mechanism of discrete preocess and the correction method of the calculated stress results are studied by theoretical deduction and a display method of the corrected stress results is proposed. Finally, a probe inside the turboprop is taken as an example to analyze the variation of buckling load and structure geometric features thoroughly, which lays a foundation for structure stability analysis and optimization.
2. Research on the finite element method for analyzing thin-walled structures under foundation vibration
The dissertation proposes a new method named static inertia method to calculate the structural response under foundation vibration with FEM by theoretical deduction. The original problem is transformed into an ordinary vibration problem with fixed base by applying the equivalent nodal loads from the new method and the response results can be calculated accordingly. The new method overcomes the restrictions of existing methods and provides a new thought to handle the problems under flush and anharmonic vibration from the base.
3. Research on the fatigue life prediction of thin-walled structures and display method of fatigue lives
Based on the cumulative fative damage theory, the dissertation estabilishes a procedure for fatigue life prediction of thin-walled structures under quasi-static and dynamic loads as well as a display method of fatigue lives with FEM package. Moreover, A program is developed accordingly and a probe is taken as an example to verify the procedure and the display method. The results indicate that the procedure above is effective and the display method is feasible.
4.Research on the fatigue crack growth (FCG) model and prediction method of thin-walled structures
The dissertation presents a new model named integrative influence factor model (IIF) to account for the intergrative influence of specimen thickness, cyclic stress ratio, material property and so forth on FCG rates by analyzing the characteristics of existing models and experimental results. Furthermore, predictions of the crack opening ratioγand effective stress intensity factor range ratio U by Newman, Huang and Codrington models are used to validate the IIF model, which indicates that the IIF model predicts the results more accurately and describes the influence of Poisson’s ratio, specimen thickness, R ratio and so on explicitly. In addition, a general model of fatigue crack growth in ductile alloys under variable amplitude loading is developed based on the IIF model and Passivation-Lancet theory. Several sets of test data are used to validate the general model and the predictions are in good agreement with the test data.
5.Research on the numerical simulation method of FCG process
In the dissertation, a new procedure of numerical simulation of FCG process under constant and variable amplitude loading is established via extended finite element method (XFEM), level set method and the general model in part 4. In addition, a matrix update algorithm based on LDU decomposition is introduced. After that, the validity of the procedure and the matrix updata algorithm are verified with several sets of test data from academic publications, which shows great consistency.
6. Research on the redevelopment of ANSYS package for numerical simulation and fatigue life prediction of thin-walled structures
The dissertation proposes a method for secondary development of ANSYS package based on the conclusions in part 1~5 and a special software for numerical simulation and fatigue life prediction of probes is developed accordingly.
The originalities of this dissertation are summarized as follows:
1. Estabilishment of the static inertia method for simulation of the continua responses under foundation vibration
This method overcomes the restrictions of existing models and can be extended to the problems under single- and multi-points anharmonic vibration from the base, flush, transient loading and so on.
2. Development of the IIF model to account for the influence of Poisson’s ratio, specimen thickness, R ratio and so forth on FCG rates The IIF model describes the influece of material property, specimen dimensions, cyclic stress ratio and so forth onγ, U and FCG rates explicitly. Furthermore, the fatigue property of real structures and specimens can be estimated by substituting the geometric parameter, experimental conditions and material parameter into IIF model. It is very helpful for fatigue tests, specimen selection and real application.
3. Estabilishment of the general model for FCG rates under constant and variable amplitude loading
The model describes the retardation and acceleration effect of single overloading, single underloading, sequential loading and spetrum loading effectively and quantitatively, owns explicit physical meaning and is suitable for modeling the FCG process of structures with various ductile materials under different loading conditions.
4. Development of a numerical simulation procedure of FCG process with XFEM and a new matrix update algorithm for equilibrium equation
The procedure inherits the advantages of level set method and XFEM, and describes the FCG process of real structures effectively. In addition, the whole continua domain is divided into two parts by the level set functions in the procedure, only the nodal data in updating region needs to be calculated and integrated, which improves the computational efficiency significantly.
1.薄壁结构响应特性有限元模拟及误差修正方法研究
基于薄壁结构的控制方程和有限元离散原理,系统研究了包含倒角、凸台、孔洞等特征的曲面薄壁结构的有限元离散特点和建模方法。同时基于离散过程的理论推导,研究了有限尺寸曲面薄壁结构的离散误差产生机理和计算应力的修正方法。以探针为对象,分析了曲面薄壁结构的屈曲载荷随几何尺寸和外形的变化规律,为结构稳定性分析和优化奠定了基础。
2.薄壁结构基础振动数值计算方法研究
基于连续体基础振动原理和有限元实现过程,建立了求解薄壁结构简谐基础振动和冲击问题的静力等效载荷法。通过施加静力等效节点载荷将简谐基础振动问题转化为基础固定的简谐响应问题,进而获得结构响应的幅值和时间历程,克服了现有方法的不足。
3.薄壁结构疲劳裂纹形成寿命预测及结果显示方法研究
基于疲劳累积损伤理论,建立了准静态和动态载荷作用下薄壁结构疲劳裂纹形成寿命的预测方法和有限元模拟及显示流程。同时以探针为对象,基于四点雨流计数法和双线性累积损伤准则,通过自编程序实现了薄壁结构疲劳寿命的自动预测和结果的图形化显示。
4.薄壁结构疲劳裂纹扩展寿命理论模型和预测方法研究
通过现有疲劳裂纹扩展速率影响因素特点和试验数据规律的研究,提出了描述试样厚度、循环应力比和材料参数等对疲劳裂纹扩展速率影响的综合影响系数模型。通过与Newman、Huang和Codrington模型对裂纹张开应力和有效应力强度因子范围比预测结果的对比,验证了模型的有效性。基于综合影响系数模型和钝化复锐理论开发了常幅和变幅载荷下疲劳裂纹扩展的通用模型,并通过试验数据和现有模型的预测结果验证了通用模型的有效性。
5.薄壁结构疲劳裂纹扩展过程数值模拟方法研究
基于第4部分的理论模型,采用扩展有限元和水平集法建立了常幅和变幅载荷下疲劳裂纹扩展过程的扩展有限元模拟流程和矩阵更新算法,并通过现有试验数据验证了理论模型、扩展有限元模拟流程和求解算法的有效性。
6.基于ANSYS的薄壁结构数值仿真和疲劳寿命预测专用软件开发
基于第1~5部分的研究成果,并以探针应用需求出发,开发了薄壁结构响应特性专用仿真和疲劳寿命预测软件。
本论文取得的主要创新成果如下:
1.提出了求解连续体简谐基础振动和冲击问题的静力等效载荷法该方法避免了瞬态计算方法中存在刚体位移、算法稳定性、模型规模等限制,以及反映谱法存在振形峰值组合规则的限制,可用于求解单点和多点非正弦(余弦)基础振动、冲击和瞬态响应等问题。
2.建立了反映材料特性、试样尺寸、载荷特征等参数对疲劳裂纹扩展速率影响的综合影响系数模型
该模型显式反映了材料特性、试样尺寸、循环应力比等因素对裂纹张开比和
有效应力强度因子范围比及疲劳裂纹扩展速率的影响。通过代入试样参数、试验条件和材料参数可预估结构和试样的疲劳特性,可为试验设计、试样选型和实际应用提供指导。
3.提出了常幅和变幅载荷下结构疲劳裂纹扩展过程的通用模型
该模型能有效且定量描述单峰过载、单峰低载、序列加载和谱载荷等产生的延迟和加速效应,具有明确的断裂力学的物理含义,适用于描述各种韧性材料、不同加载条件和不同试样类型的疲劳裂纹扩展过程。
4.建立了结构疲劳裂纹扩展过程的扩展有限元模拟流程和平衡方程更新算法该流程能有效模拟实际结构的疲劳裂纹扩展过程,同时通过水平集函数将模型分割为更新和非更新区域,疲劳裂纹扩展过程中仅需对更新区域的数据进行计算和集成,大大提高了求解效率。
Thin-walled structures are widely used in aeronautics, watercrafts, automobiles, vessels and so on because of its light weight and good load-carring property. But the theoretical stress and strain results of these structures can be hardly derived due to the influence of geometrical shape, boundary conditions and so on. Hence, the basic theory and numcerical simulation methods of these structures have been the research focus for decades. In the dissertation, the following topics are studied based on the problems existing in numerical simulation, stability analysis and fatigue life prediction:
1. Research on the finite element modeling method and error correction method of the response characteristics of thin-walled structures
The modeling method and discrete characteristics of curved thin-walled structures with chamfers, bosses, holes and so on are studied systematically based on its governing equations and the discrete principles of finite element method (FEM) at first. Then, the error mechanism of discrete preocess and the correction method of the calculated stress results are studied by theoretical deduction and a display method of the corrected stress results is proposed. Finally, a probe inside the turboprop is taken as an example to analyze the variation of buckling load and structure geometric features thoroughly, which lays a foundation for structure stability analysis and optimization.
2. Research on the finite element method for analyzing thin-walled structures under foundation vibration
The dissertation proposes a new method named static inertia method to calculate the structural response under foundation vibration with FEM by theoretical deduction. The original problem is transformed into an ordinary vibration problem with fixed base by applying the equivalent nodal loads from the new method and the response results can be calculated accordingly. The new method overcomes the restrictions of existing methods and provides a new thought to handle the problems under flush and anharmonic vibration from the base.
3. Research on the fatigue life prediction of thin-walled structures and display method of fatigue lives
Based on the cumulative fative damage theory, the dissertation estabilishes a procedure for fatigue life prediction of thin-walled structures under quasi-static and dynamic loads as well as a display method of fatigue lives with FEM package. Moreover, A program is developed accordingly and a probe is taken as an example to verify the procedure and the display method. The results indicate that the procedure above is effective and the display method is feasible.
4.Research on the fatigue crack growth (FCG) model and prediction method of thin-walled structures
The dissertation presents a new model named integrative influence factor model (IIF) to account for the intergrative influence of specimen thickness, cyclic stress ratio, material property and so forth on FCG rates by analyzing the characteristics of existing models and experimental results. Furthermore, predictions of the crack opening ratioγand effective stress intensity factor range ratio U by Newman, Huang and Codrington models are used to validate the IIF model, which indicates that the IIF model predicts the results more accurately and describes the influence of Poisson’s ratio, specimen thickness, R ratio and so on explicitly. In addition, a general model of fatigue crack growth in ductile alloys under variable amplitude loading is developed based on the IIF model and Passivation-Lancet theory. Several sets of test data are used to validate the general model and the predictions are in good agreement with the test data.
5.Research on the numerical simulation method of FCG process
In the dissertation, a new procedure of numerical simulation of FCG process under constant and variable amplitude loading is established via extended finite element method (XFEM), level set method and the general model in part 4. In addition, a matrix update algorithm based on LDU decomposition is introduced. After that, the validity of the procedure and the matrix updata algorithm are verified with several sets of test data from academic publications, which shows great consistency.
6. Research on the redevelopment of ANSYS package for numerical simulation and fatigue life prediction of thin-walled structures
The dissertation proposes a method for secondary development of ANSYS package based on the conclusions in part 1~5 and a special software for numerical simulation and fatigue life prediction of probes is developed accordingly.
The originalities of this dissertation are summarized as follows:
1. Estabilishment of the static inertia method for simulation of the continua responses under foundation vibration
This method overcomes the restrictions of existing models and can be extended to the problems under single- and multi-points anharmonic vibration from the base, flush, transient loading and so on.
2. Development of the IIF model to account for the influence of Poisson’s ratio, specimen thickness, R ratio and so forth on FCG rates The IIF model describes the influece of material property, specimen dimensions, cyclic stress ratio and so forth onγ, U and FCG rates explicitly. Furthermore, the fatigue property of real structures and specimens can be estimated by substituting the geometric parameter, experimental conditions and material parameter into IIF model. It is very helpful for fatigue tests, specimen selection and real application.
3. Estabilishment of the general model for FCG rates under constant and variable amplitude loading
The model describes the retardation and acceleration effect of single overloading, single underloading, sequential loading and spetrum loading effectively and quantitatively, owns explicit physical meaning and is suitable for modeling the FCG process of structures with various ductile materials under different loading conditions.
4. Development of a numerical simulation procedure of FCG process with XFEM and a new matrix update algorithm for equilibrium equation
The procedure inherits the advantages of level set method and XFEM, and describes the FCG process of real structures effectively. In addition, the whole continua domain is divided into two parts by the level set functions in the procedure, only the nodal data in updating region needs to be calculated and integrated, which improves the computational efficiency significantly.
引文
[1]关桥,郭德伦,张崇显等.航宇薄壳结构的低应力无变形焊接新技术[J].航空工艺技术, 1996(4): 4-7.
[2]张震宇,姚文娟.大圆筒薄壳结构的研究进展[J].上海大学学报(自然科学版), 2004, 10(1): 82-90.
[3]孙凌玉, Stephen B.,姚迎宪.车身薄壁梁结构轻量化设计的理论研究[J].北京航空航天大学学报, 2004, 30(12): 1163-1167.
[4]骆天明.压力容器薄壁结构的鉴定与分析[J].湖南城市学院学报(自然科学版), 2007, 16(4): 17-19.
[5]周晴.发动机测试探针振动特性有限元分析系统的研究与开发[D].成都:电子科技大学, 2010.
[6]黄明镜.受感部力学特性数值模拟方法研究[D].成都:电子科技大学, 2009.
[7]向宏辉,任铭林,马宏伟等.叶型探针对轴流压气机性能试验结果的影响[J].燃气涡轮试验与研究, 2008, 21(4): 28-33.
[8]高光藩,丁信伟.薄壳结构分析有限元方法[J].石油化工设备, 2002, 31(5): 28-32.
[9] Yang H.T.Y., Saigal S., Liaw D.G. Advances of thin shell finite elemtns and some applictions version[J]. Computer & structure, 1990, 35(4): 481-504.
[10] Duran R.G., Hernandez E., Hervella-Nieto L., et al. Error estimaties for low-order isoparametric quadrilateral finite elements for plates[J]. SIAM : journal on numerical analysis, 2003, 41(5): 1751-1772.
[11] Mousa A.I., ElNaggar M.H. Shallow spherical shell rectangular finite element for analysis of cross shaped shell roof[J]. Electronic journal of structural engineering, 2007, 7: 41-51.
[12]岑松,龙驭球.采用面积坐标的四边形厚薄板通用单元[J].工程力学, 1999, 16(2): 1-15.
[13]龙驭球,陈晓明,岑松.一个不闭锁和抗畸变的四边形厚板元[J].计算力学学报, 2005, 22(4): 385-391.
[14]王丽,龙志飞,龙驭球.混合应用三类四边形面积坐标构造八节点四边形膜元[J].工程力学, 2010, 27(2): 1-6.
[15] Baginski F.E. The computation of one parameter families of bifurcating elastic surfaces[J]. SIAM : journal on numerical analysis, 1994, 54(3): 738-773.
[16] Carr S.M., Lawrence W.E., Wybourne M.N. Static buckling and actuation of free-standing mesoscale beams[J]. IEEE transactions on nanotechnology, 2005, 4(6): 655-659.
[17]肖刚.结构在约束下和动力作用下屈曲的数值模拟[D].上海:上海交通大学, 2008.
[18]李峰,马旭.周边局部双层球面网格特征值屈曲分析[J].低温建筑技术, 2011, 159: 52-53.
[19] Liu Y.X., Li X., Zhou J. Analysis study of imperfect pipeline on lateral buckling[J]. Journal of ship mechanics, 2011, 15(9): 1033-1040.
[20]吴轶,莫海鸿,杨春.大型拱式U型薄壁渡槽结构的模态分析[J].华南理工大学学报(自然科学版), 2003, 31(3): 72-76.
[21]汪苏,王春侠,郭军刚.航空发动机薄壁机匣激光焊接有限元数值模拟[J].北京航空航天大学学报, 2006, 32(7): 833-837.
[22]马春生,杜汇良,张金换等.薄壁扁球壳结构在撞击载荷作用下的变形控制方法研究[J].振动与冲击, 2007, 26(4): 10-13.
[23]王晓波,李凤琴.含有轴向裂纹的圆柱薄壳的模态分析[J].黄河水利职业技术学院学报, 2011, 23(2): 36-38.
[24]靖建朋,郭荣伟.气动变形对独立模块薄壳进气道性能影响研究[J].宇航学报, 2011, 32(1): 210-218.
[25] Morel F. A critical plane approach for life predition of high cycle fatigue under multiaxial variable amplitude loading [J]. International journal of fatigue, 2000, 22(2): 101-119.
[26]赵东拂.混凝土多周疲劳破坏准则研究[D].大连:大连理工大学, 2002.
[27]尚德广,王大康,孙国芹等.多轴疲劳裂纹扩展行为研究[J].机械强度, 2004, 26(4): 423-427.
[28]王英玉.金属材料的多轴疲劳行为与寿命估算[D].南京:南京航空航天大学, 2005.
[29] Sun G., Shang D., Bao M. Multiaxial fatigue damage parameter and life prediction under low cycle loading for GH4169 alloy and other structural materials[J]. International journal of fatigue, 2010, 32(7): 1108-1115.
[30] Yung J.Y., Lawrence F.V. Analytical and graphical aids for the fatigue design weldments[J]. Fatigue & Fracture of engineering materials & structures, 1985, 8(3): 223-241.
[31] Andrews R.M. The effect of misalignment on the fatigue strength of welded cruciform joints[J]. Fatigue & Fracture of engineering materials & structures, 1996, 19: 755-768.
[32]路金花.基于CSR的船体结构强度分析和焊趾处疲劳强度分析[D].哈尔滨:哈尔滨工程大学, 2007.
[33]李晓峰.基于虚拟疲劳试验的铁路车辆焊接结构疲劳寿命预测[D].大连:大连交通大学,2008.
[34] Varschavsky A. The matrix fatigue behaviour of fibre coposites subjected to repeated tensile loads[J]. Journal of materials science, 1972, 7: 159-167.
[35] Xia Z.H., Peters P.W.M., Dudek H.J. Finite element modelling of fatigue crack initiation in SiC-fibre reinforced titanium alloys[J]. Composites: Part A, 2000, 31: 1031-1037.
[36]齐红宇.复合材料及发动机机匣的屈曲与疲劳研究[D].南京:南京航空航天大学, 2001.
[37] Hosseini-Toudeshky H. Effects of composite patches on fatigue crack propagation of single-side repaired aluminum panels[J]. Composite structure, 2006, 76: 243-251.
[38]王放.金属基复合材料循环响应和疲劳破坏的理论和模拟[D].上海:上海大学, 2007.
[39] Funkenbusch A.W., Coffin L.F. Low cycle fatigue crack numcleation and early growth in Ti-17[J]. Metallurgical transations A, 1978, 9A: 1159-1167.
[40] Yong J.O., Soo N.W. Low cycle fatigue crack advance and life prediction[J]. Journal of materials science, 1992, 27: 2019-2025.
[41]丁智平.复杂应力状态镍基单晶高温合金低周疲劳损伤研究[D].长沙:中南大学, 2005.
[42]高红.无铅钎料Sn-3.5多轴棘轮变形与低周疲劳研究[D].天津:天津大学, 2007.
[43]王弘. 40Cr、50车轴钢超高周疲劳性能研究及疲劳断裂机理探讨[D].成都:西南交通大学, 2004.
[44]邵红红. 40CrNiMoA钢超高周疲劳行为研究[D].南京:南京理工大学, 2007.
[45] Shiozawa K., Hasegawa T., Kashiwagi Y.,et al. Very high cycle fatigue properties of bearing steel under axial loading condition[J]. International journal of fatigue, 2009, 31: 880-888.
[46]王泓.材料疲劳裂纹扩展和断裂定量规律的研究[D].西安:西北工业大学, 2002.
[47] Paris P., Erdogan F. A critical analysis of crack growth laws[J]. Journal of Basic Engineering, 1963, 85(3): 528-534.
[48] Forman R.G., Kearney V.E., Engle R.M. Numerical analysis of crack propagation in cyclic-loaded structure[J]. Journal of Basic Engineering, 1967, 89(3): 459-464.
[49] Elber W. The significance of fatigue crack closure in Damage tolerate in aircraft structures. ASTM STP486, American society for testing and material: Philadophia, 1971: 230-242.
[50] Richards C.E., Lindley T.C. The influence of stress intensity and microstructure on fatigue crack propagation in feritic materials[J]. Engineering Fracture Mechanics, 1972, 4(7): 951-978.
[51]张平生,胡志忠,蔡和平等.一种疲劳裂纹扩展速率da/dN的表达式[J].西安交通大学学报, 1982, 16(1): 33-42.
[52]赵永翔,杨冰,张卫华.一种疲劳长裂纹扩展速率新模型[J].机械工程学报, 2006, 42(11):120-124.
[53]杨冰,赵永翔,梁红琴等.基于Elber型方程的随机疲劳长裂纹扩展概率模型[J].工程力学, 2005, 22(5): 99-104.
[54] McMaster F.J., Smith D.J. Predictions of fatigue crack growth in aluminium alloy 2024-T351 using constraint factors[J]. International journal of fatigue, 2001, 23: S93-S101.
[55] Huang X.P., Torgeir M., Cui W.C. An engineering model of fatigue crack growth under variable amplitude loading [J]. International journal of fatigue, 2008, 30: 2-10.
[56] Yi G.J., Wang Y.F., Cui W.C., et al. Application of the general fatigue crack growth model on the single overload fatigue problem[J]. Journal of ship mechanics, 2008, 12: 947-954.
[57] Patankar R., Ray A., Lakhtakis A. A state space model of fatigue crack growth[J]. International journal of fracture, 1998, 90: 235-249.
[58] Qu R., Patankar R.P., Rao M.D. A third-order state space model fro fatigue crack growth[J]. Fatigue & Fracture of engineering materials & structures, 2006, 29: 1045-1055.
[59] Shahinian P. Influence of section thickness on fatigue crack growth in type 304 stainless steel[J]. Nuclear technology, 1972, 30: 390-397.
[60] Jack A.R., Price A.T. Effect of thickness on fatigue crack initiation and growth in notched mild-steel specimens[J]. Acta metallurgica, 1972, 20: 857-866.
[61] Costa J.D.M., Ferreira J.A.M. Effect of stress ratio and specimen thickness on fatigue crack growth of CK45 steel[J]. Theoretical and applied fracture mechanics, 1998, 30: 65-70.
[62] Park H.B., Lee B.W. Effect of specimen thickness on fatigue crack growth rate[J]. Nuclear Engineering and design, 2000, 197(1-2): 197-203.
[63] Wang J., Gao J.X., Guo W.L., et al. Effects of specimen thickness, hardening and crack closure for the plastic strip model[J]. Theoretical and applied fracture mechanics, 1998, 29: 49-57.
[64] Jen Y.,Chang L. Effects of thickness of face sheet on the bending fatigue strength of aluminum honeycomb sandwich beams[J]. Engineering Fracture Mechanics, 2009, 16: 1282-1293.
[65] Shipilov S.A. Effects of stress ratio on the mechanism of environmentally-assisted fatigue crack growth in high strength steels[J]. Strenght of materials, 1995, 27(1-2): 64-69.
[66] Chang T., Li G., Hou J. Effects of applied stress level on plastic zone size and opening stress ratio of a fatigue crack[J]. International journal of fatigue, 2005, 27: 519-526.
[67] Newman J.C., Ruschau J.J. The stress level effect on fatigue crack growth under constant amplitude loading[J]. International journal of fatigue, 2007, 29: 1608-1615.
[68] Runt J., Gallagher K.P. The influence of microstructure on fatigue crack propagation inpolyoxymethylene[J]. Journal of materials science, 1991, 26: 792-798.
[69] Fonte M.A., Stanzl-Tschegg S.E., Holper B., et al. The microstructure and enviroments influence on fatigue crack growth in 7049 aluminum alloy at different load ratios[J]. International journal of fatigue, 2001, 23: S311-S317.
[70] Saengsai A., Miyashita Y., Mutoh Y. Effects of humidity and contact material on fretting behavior of an extruded AZ61 magnesium alloy[J]. Tribology international, 2009, 42(9): 1346-1351.
[71]傅惠民,高镇同. a-N(a-t)曲线三参数米函数拟合法[J].航空学报, 1989, 10(12): B666-B670.
[72]傅惠民,高镇同.给定寿命下的疲劳裂纹尺寸分布[J].航空学报, 1988, 9(3): A113-A118.
[73]田秀云,孙智强. 2024-T2铝合金疲劳裂纹扩展曲线的拟合方法研究[J].航空学报, 2003, 24(2): 144-146.
[74]王红军,徐人平.常用a-N曲线拟合方法的比较[J].机械, 2009, 36(2): 24-25.
[75] Erdogan F., Sih G.C. On the extension in plates under plane loading and transverse shear[J]. Journal of Basic Engineering, 1963: 519-527.
[76]牟宗花,杜善义,张泽华.拉压强度不同材料的复合型断裂准则[J].哈尔滨工业大学学报, 1995, 27(6): 38-41.
[77] Skelton R.P., Vilhelmsen T., Webster G.A. Energy criteria and cumulative damage during fatigue crack growth[J]. International journal of fatigue, 1998, 20(9): 641-649.
[78]刘小妹,刘一华,梁拥成等.复合型V形切口脆断的应变能密度因子准则[J].机械强度, 2008, 30(2): 288-292.
[79]淳庆.应力强度因子和裂纹扩展判据的典型算法[J].江苏大学学报(自然科学版), 2011, 32(3): 354-358.
[80] Melenk J.M., Babuska I. the partition of unity finite element method: basic theory and applications[J]. Computer methods in applied mechanics and engineering, 1996, 139: 289-314.
[81] Belytschko T., Black T. Elastic crack growth in finite elements with minimal remeshing[J]. International journal for numerical methods in engineering, 1999, 45: 601-620.
[82] Moes N., Dolbow J., Belytschko T. A finite element method for crack growth without remeshing[J]. International journal for numerical methods in engineering, 1999, 46: 131-150.
[83] Dolbow J., Moes N., Belytschko T. Discontinuous enrichment in finite elements with a partition of unity method[J]. Finite elements in analysis and design, 2000, 36: 235-260.
[84] Daux C., Moes N., Dolbow J.,et al. Arbitrary branched and intersecting cracks with theextended finite element method[J]. International journal for numerical methods in engineering, 2000, 48: 1741-1760.
[85] Belytschko T., Moes N., Usui S., et al. Arbitrary discontinuities in finite elements[J]. International journal for numerical methods in engineering, 2001, 50: 993-1013.
[86] Sukumar N., Chopp D.L., Moes N.,et al. Modelling holes and inclusions by level sets in the extended finite element method[J]. Computer methods in applied mechanics and engineering, 2001, 190: 6183-6200.
[87] Belytschko T., Gracie R., Ventura G. A review of extended/generalized finite element methods for material modeling[J]. Modeling and simulation in materials science and engineering, 2009, 17: 1-24.
[88] Bechet E., Minnebo H., Moes N., et al. Improved implementation and robustness study of the X-FEM for stres analysis around cracks[J]. International journal for numerical methods in engineering, 2005, 64: 1033-1056.
[89] Laborde P., Pommier J., Renard Y., et al. High order extended finite element method for cracked domains[J]. International journal for numerical methods in engineering, 2005, 64: 354-381.
[90] Xiao Q.Z., Karihaloo B.L. Improving the accuracy of XFEM crack tip field using higher order quadrature and statically admissible stress recovery[J]. International journal for numerical methods in engineering, 2006, 66(9): 1378-1410.
[91] Liu X.Y., Xiao Q.Z., Karihaloo B.L. XFEM for direct evaluation of mixed mode SIFs in homogeneous and bi-materials[J]. International journal for numerical methods in engineering, 2004, 59: 1103-1118.
[92] Xiao Q.Z., Karihaloo B.L., Liu X.Y. Incremental-secant modulus iteration scheme and stress recovery for simulating cracking process in quasi-brittle materials using XFEM[J]. International journal for numerical methods in engineering, 2007, 69: 2606-2635.
[93] Wyart E., Coulon D., Duflot M., et al. A substructured FE-shell/XFEM-3D method for crack analysis in thin-walled structures[J]. International journal for numerical methods in engineering, 2007, 72: 757-779.
[94] Osher S., Sethian J.A. Front propagating with curvature dependent speed: algorithms based on Hamilton-Jacobi formulations[J]. Journal of computational physics, 1988, 79: 12-49.
[95] Sethian J.A. Level set methods and fast marching methods: Evolving interfaces in computational geometry, fluid mechanics[M]. Cambridge Cambridge university press, 1999.
[96] Stolarska M., Chopp D.L., Moes N., et al. Modelling crack growth by level sets in the extendedfinite element method[J]. International journal for numerical methods in engineering, 2001, 51: 943-960.
[97] Moes N., Gravouil A., Belytschko T. Non-planar 3D crack growth by the extended finite element and level sets-part I mechanical model[J]. International journal for numerical methods in engineering, 2002, 53(11): 2549-2568.
[98] Chopp D.L., Sukumar N. Fatigue crack propagation of multiple coplanar cracks with the coupled extended finite element and fast marching method[J]. International journal of engineering science, 2003, 41(8): 845-869.
[99]方修君,金峰.基于ABAQUS平台的扩展有限元法[J].工程力学, 2007, 24(7): 6-10.
[100] Shi J., Chopp D., Lua J., et al. Abaqus implementation of extended finite element method using a level set respresentation for three dimensional fatigue crack growth and life predictions[J]. Engineering Fracture Mechanics, 2010, 77: 2840-2863.
[101]李录贤,王铁军.扩展有限元法(XFEM)及其应用[J].力学进展, 2005, 35(1): 5-20.
[102]余天堂.含裂纹体的数值模拟[J].岩石力学与工程学报, 2005, 24(24): 4434-4439.
[103]余天堂.扩展有限元法的数值方面[J].岩土力学, 2007, 28(增刊): 305-310.
[104]董玉文,余天堂,任青文.直接计算应力强度因子的扩展有限元法[J].计算力学学报, 2008, 25(1): 72-77.
[105]喻葭临,张其光,于玉贞等.扩展有限元中非连续区域的一种积分方案[J].清华大学学报(自然科学版), 2009, 49(3): 351-354.
[106]刘波波.基于时域精细算法与扩展有限元技术的粘弹性位移场分析[D].大连:大连理工大学, 2009.
[107]朱传锐.基于扩展有限元和水平集理论的裂纹扩展问题研究[D].焦作:河南理工大学, 2010.
[108]陈连玉,周东清,郭锦华.国外引进软件二次开发的若干技术问题[J].大连理工大学学报, 1999, 39(5): 706-709.
[109]谢配良,薛海,盛伟. ANSYS软件的二次开发及其在大容量缓冲器模锻件上的应用[J].微机应用, 2000, 6: 26-28.
[110]齐慧,杨屹,蒋玉明.基于ANSYS软件二次开发的铸造充型和凝固耦合过程数值模拟研究[J].四川大学学报(工程科学版), 2001, 33(5): 47-50.
[111]陈文.基于灵敏度与模拟退火方法的模型修正及软件二次开发[D].南京:南京航空航天大学, 2008.
[112]徐飞英. ADINA软件二次开发初探[J].江西化工, 2008, 1: 138-140.
[113]曹琳,赵继伟. ADINA软件的二次开发[J].人民黄河, 2009, 31(7): 96-97.
[114]李健,杨坤.基于ABAQUS软件二次开发技术筒形件旋压过程研究[J].锻压技术, 2009, 34(6): 129-132.
[115]刘建涛,杜平安,黄明镜等.曲面薄壳有限元离散误差分析和修正方法研究[J].系统仿真学报, 2010, 22(10):2281-2286.
[116]刘长福,邓明.航空发动机结构分析[M].西安:西北工业大学出版社, 2005.
[117] You J.F., Chen R.X. Buckling analysis on rear dome of solid rocket motor case[J]. Journal of Solid Rocket Technology, 2008, 31(2): 173-178.
[118]懂永辉,况雨春,伍开松等.弯曲井眼中钻柱屈曲的非线性有限元分析[J].石油机械, 2008, 36(4): 25-27.
[119]任建峰,仇原鹰,段宝岩等.一种基础加速度冲击的仿真新方法[J].现代机械, 2006, 2: 21-23.
[120] Chopra A.K. (著),谢礼立,吕大刚(译).结构动力学理论及其在地震工程中的应用[M].北京:高等教育出版社, 2005.
[121]管德清.焊接钢结构疲劳强度与寿命预测理论的研究[D].长沙:湖南大学, 2003.
[122] Lee Y.L., Pan J., Hathaway R.B., et al. Fatigue testing and analysis (Theory and practice)[M]. Burlington: Elsevier Butterworth-Heinemann, 2005.
[123]赵建生.断裂力学及断裂物理[M].武昌:华中科技大学出版社, 2006.
[124]董慧茹,郭万林.复合型裂纹起裂角厚度效应的实验研究[J].工程力学, 2004, 21(4):123-127.
[125] Zhao T.W., Zhang J.X., Jiang Y.Y. A study of fatigue crack growth of 7075-T651 aluminum alloy[J]. International journal of fatigue, 2008, 30: 1169-1180.
[126] Ray A., Patankar R. Fatigue crack growth under variable-amplitude loading: part I-model formulation in state space setting[J]. Applied mathematical modeling, 2001, 25: 979-994.
[127] Lee E.U., Vasudevan A.K., Sadananda K. Effects of various environments on fatigue crack growth in Laser formed and IM Ti-6Al-4V alloys[J]. International journal of fatigue, 2005, 27: 1597-1607.
[128]高艳丽. 16Mn钢焊接件疲劳裂纹萌生与扩展的研究[D].沈阳:沈阳大学, 2007.
[129] Newman J.C. A crack opening stress equation for fatigue crack growth[J]. International journal of fracture, 1984, 24: R131-R135.
[130] Huang X.P., Han Y., Cui W.C., et al. Fatigue life prediction of weld-joints under variable amplitude fatigue loads[J]. Journal of ship mechanics, 2005, 9(1): 89-97.
[131] Codrington J., Kotousov A. A crack closure model of fatigue crack growth in plates of finite thickness under small scale yielding conditions[J]. Mechanics of materials, 2009, 41: 165-173.
[132] Hsu K., Lin C. Effects of R ratio on high temperature fatigue crack growth behavior of a precipitation-hardening stainless steel[J]. International journal of fatigue, 2008, 30: 2147-2155.
[133] Paris P.C., Tada H., Donald J.K. Service load fatigue damage——a historical perspective[J]. International journal of fatigue, 1999, 21: S35-S46.
[134] Voorwald H.J.C., Torres M.A.S., Junior C.C.E.P. Modeling of fatigue crack growth following overloads[J]. International journal of fatigue, 1991, 13: 423-427.
[135] Liu J.T., Du P.A., Huang M.J., et al. New model of propagation rates of long crack due to structure fatigue[J]. Applied mathematics and mechanics, 2009, 30(5): 575-584.
[136] Chang T., Guo W. A model for the through-thickness fatigue crack closure[J]. Engineering Fracture Mechanics, 1999, 64: 59-65.
[137] Porter T.R. Method of analysis and prediction for variable amplitude fatigue crack growth[J]. Engineering Fracture Mechanics, 1972, 4: 717-736.
[138] Yisheng W., Schijve J. Fatigue crack closure measurements on 2024-T3 sheet specimens[J]. Fatigue & Fracture of engineering materials & structures, 1995, 18(9): 917-921.
[139] Comi C., Mariani S. Extended finite lement simulation of quasi-brittle fracture in functionally graded materials[J]. Computer methods in applied mechanics and engineering, 2007, 196: 4013-4026.
[140]方修君,金峰,王进廷.基于扩展有限元法的Koyna重力坝地震开裂过程模拟[J].清华大学学报(自然科学版), 2008, 48(12): 2065-2069.
[141] Pais M. J. Accurate integration of fatigue crack growth models through kriging and reanalysis of the extended finite elemtn method[D]. Gainesville: University of Florida, 2010.
[142] Babuska I., Zhang Z.M. The partition of unity method for the elastically supported beam[J]. Computer methods in applied mechanics and engineering, 1998, 152(1-2): 1-18.
[143] Williams M. On the stress distribution at the base of a stationary crack[J]. Journal of applied mechanics, 1957, 24(1): 109-114.
[144]中国航空研究院.应力强度因子手册(增订版) [M].北京:科学出版社, 1993.
[2]张震宇,姚文娟.大圆筒薄壳结构的研究进展[J].上海大学学报(自然科学版), 2004, 10(1): 82-90.
[3]孙凌玉, Stephen B.,姚迎宪.车身薄壁梁结构轻量化设计的理论研究[J].北京航空航天大学学报, 2004, 30(12): 1163-1167.
[4]骆天明.压力容器薄壁结构的鉴定与分析[J].湖南城市学院学报(自然科学版), 2007, 16(4): 17-19.
[5]周晴.发动机测试探针振动特性有限元分析系统的研究与开发[D].成都:电子科技大学, 2010.
[6]黄明镜.受感部力学特性数值模拟方法研究[D].成都:电子科技大学, 2009.
[7]向宏辉,任铭林,马宏伟等.叶型探针对轴流压气机性能试验结果的影响[J].燃气涡轮试验与研究, 2008, 21(4): 28-33.
[8]高光藩,丁信伟.薄壳结构分析有限元方法[J].石油化工设备, 2002, 31(5): 28-32.
[9] Yang H.T.Y., Saigal S., Liaw D.G. Advances of thin shell finite elemtns and some applictions version[J]. Computer & structure, 1990, 35(4): 481-504.
[10] Duran R.G., Hernandez E., Hervella-Nieto L., et al. Error estimaties for low-order isoparametric quadrilateral finite elements for plates[J]. SIAM : journal on numerical analysis, 2003, 41(5): 1751-1772.
[11] Mousa A.I., ElNaggar M.H. Shallow spherical shell rectangular finite element for analysis of cross shaped shell roof[J]. Electronic journal of structural engineering, 2007, 7: 41-51.
[12]岑松,龙驭球.采用面积坐标的四边形厚薄板通用单元[J].工程力学, 1999, 16(2): 1-15.
[13]龙驭球,陈晓明,岑松.一个不闭锁和抗畸变的四边形厚板元[J].计算力学学报, 2005, 22(4): 385-391.
[14]王丽,龙志飞,龙驭球.混合应用三类四边形面积坐标构造八节点四边形膜元[J].工程力学, 2010, 27(2): 1-6.
[15] Baginski F.E. The computation of one parameter families of bifurcating elastic surfaces[J]. SIAM : journal on numerical analysis, 1994, 54(3): 738-773.
[16] Carr S.M., Lawrence W.E., Wybourne M.N. Static buckling and actuation of free-standing mesoscale beams[J]. IEEE transactions on nanotechnology, 2005, 4(6): 655-659.
[17]肖刚.结构在约束下和动力作用下屈曲的数值模拟[D].上海:上海交通大学, 2008.
[18]李峰,马旭.周边局部双层球面网格特征值屈曲分析[J].低温建筑技术, 2011, 159: 52-53.
[19] Liu Y.X., Li X., Zhou J. Analysis study of imperfect pipeline on lateral buckling[J]. Journal of ship mechanics, 2011, 15(9): 1033-1040.
[20]吴轶,莫海鸿,杨春.大型拱式U型薄壁渡槽结构的模态分析[J].华南理工大学学报(自然科学版), 2003, 31(3): 72-76.
[21]汪苏,王春侠,郭军刚.航空发动机薄壁机匣激光焊接有限元数值模拟[J].北京航空航天大学学报, 2006, 32(7): 833-837.
[22]马春生,杜汇良,张金换等.薄壁扁球壳结构在撞击载荷作用下的变形控制方法研究[J].振动与冲击, 2007, 26(4): 10-13.
[23]王晓波,李凤琴.含有轴向裂纹的圆柱薄壳的模态分析[J].黄河水利职业技术学院学报, 2011, 23(2): 36-38.
[24]靖建朋,郭荣伟.气动变形对独立模块薄壳进气道性能影响研究[J].宇航学报, 2011, 32(1): 210-218.
[25] Morel F. A critical plane approach for life predition of high cycle fatigue under multiaxial variable amplitude loading [J]. International journal of fatigue, 2000, 22(2): 101-119.
[26]赵东拂.混凝土多周疲劳破坏准则研究[D].大连:大连理工大学, 2002.
[27]尚德广,王大康,孙国芹等.多轴疲劳裂纹扩展行为研究[J].机械强度, 2004, 26(4): 423-427.
[28]王英玉.金属材料的多轴疲劳行为与寿命估算[D].南京:南京航空航天大学, 2005.
[29] Sun G., Shang D., Bao M. Multiaxial fatigue damage parameter and life prediction under low cycle loading for GH4169 alloy and other structural materials[J]. International journal of fatigue, 2010, 32(7): 1108-1115.
[30] Yung J.Y., Lawrence F.V. Analytical and graphical aids for the fatigue design weldments[J]. Fatigue & Fracture of engineering materials & structures, 1985, 8(3): 223-241.
[31] Andrews R.M. The effect of misalignment on the fatigue strength of welded cruciform joints[J]. Fatigue & Fracture of engineering materials & structures, 1996, 19: 755-768.
[32]路金花.基于CSR的船体结构强度分析和焊趾处疲劳强度分析[D].哈尔滨:哈尔滨工程大学, 2007.
[33]李晓峰.基于虚拟疲劳试验的铁路车辆焊接结构疲劳寿命预测[D].大连:大连交通大学,2008.
[34] Varschavsky A. The matrix fatigue behaviour of fibre coposites subjected to repeated tensile loads[J]. Journal of materials science, 1972, 7: 159-167.
[35] Xia Z.H., Peters P.W.M., Dudek H.J. Finite element modelling of fatigue crack initiation in SiC-fibre reinforced titanium alloys[J]. Composites: Part A, 2000, 31: 1031-1037.
[36]齐红宇.复合材料及发动机机匣的屈曲与疲劳研究[D].南京:南京航空航天大学, 2001.
[37] Hosseini-Toudeshky H. Effects of composite patches on fatigue crack propagation of single-side repaired aluminum panels[J]. Composite structure, 2006, 76: 243-251.
[38]王放.金属基复合材料循环响应和疲劳破坏的理论和模拟[D].上海:上海大学, 2007.
[39] Funkenbusch A.W., Coffin L.F. Low cycle fatigue crack numcleation and early growth in Ti-17[J]. Metallurgical transations A, 1978, 9A: 1159-1167.
[40] Yong J.O., Soo N.W. Low cycle fatigue crack advance and life prediction[J]. Journal of materials science, 1992, 27: 2019-2025.
[41]丁智平.复杂应力状态镍基单晶高温合金低周疲劳损伤研究[D].长沙:中南大学, 2005.
[42]高红.无铅钎料Sn-3.5多轴棘轮变形与低周疲劳研究[D].天津:天津大学, 2007.
[43]王弘. 40Cr、50车轴钢超高周疲劳性能研究及疲劳断裂机理探讨[D].成都:西南交通大学, 2004.
[44]邵红红. 40CrNiMoA钢超高周疲劳行为研究[D].南京:南京理工大学, 2007.
[45] Shiozawa K., Hasegawa T., Kashiwagi Y.,et al. Very high cycle fatigue properties of bearing steel under axial loading condition[J]. International journal of fatigue, 2009, 31: 880-888.
[46]王泓.材料疲劳裂纹扩展和断裂定量规律的研究[D].西安:西北工业大学, 2002.
[47] Paris P., Erdogan F. A critical analysis of crack growth laws[J]. Journal of Basic Engineering, 1963, 85(3): 528-534.
[48] Forman R.G., Kearney V.E., Engle R.M. Numerical analysis of crack propagation in cyclic-loaded structure[J]. Journal of Basic Engineering, 1967, 89(3): 459-464.
[49] Elber W. The significance of fatigue crack closure in Damage tolerate in aircraft structures. ASTM STP486, American society for testing and material: Philadophia, 1971: 230-242.
[50] Richards C.E., Lindley T.C. The influence of stress intensity and microstructure on fatigue crack propagation in feritic materials[J]. Engineering Fracture Mechanics, 1972, 4(7): 951-978.
[51]张平生,胡志忠,蔡和平等.一种疲劳裂纹扩展速率da/dN的表达式[J].西安交通大学学报, 1982, 16(1): 33-42.
[52]赵永翔,杨冰,张卫华.一种疲劳长裂纹扩展速率新模型[J].机械工程学报, 2006, 42(11):120-124.
[53]杨冰,赵永翔,梁红琴等.基于Elber型方程的随机疲劳长裂纹扩展概率模型[J].工程力学, 2005, 22(5): 99-104.
[54] McMaster F.J., Smith D.J. Predictions of fatigue crack growth in aluminium alloy 2024-T351 using constraint factors[J]. International journal of fatigue, 2001, 23: S93-S101.
[55] Huang X.P., Torgeir M., Cui W.C. An engineering model of fatigue crack growth under variable amplitude loading [J]. International journal of fatigue, 2008, 30: 2-10.
[56] Yi G.J., Wang Y.F., Cui W.C., et al. Application of the general fatigue crack growth model on the single overload fatigue problem[J]. Journal of ship mechanics, 2008, 12: 947-954.
[57] Patankar R., Ray A., Lakhtakis A. A state space model of fatigue crack growth[J]. International journal of fracture, 1998, 90: 235-249.
[58] Qu R., Patankar R.P., Rao M.D. A third-order state space model fro fatigue crack growth[J]. Fatigue & Fracture of engineering materials & structures, 2006, 29: 1045-1055.
[59] Shahinian P. Influence of section thickness on fatigue crack growth in type 304 stainless steel[J]. Nuclear technology, 1972, 30: 390-397.
[60] Jack A.R., Price A.T. Effect of thickness on fatigue crack initiation and growth in notched mild-steel specimens[J]. Acta metallurgica, 1972, 20: 857-866.
[61] Costa J.D.M., Ferreira J.A.M. Effect of stress ratio and specimen thickness on fatigue crack growth of CK45 steel[J]. Theoretical and applied fracture mechanics, 1998, 30: 65-70.
[62] Park H.B., Lee B.W. Effect of specimen thickness on fatigue crack growth rate[J]. Nuclear Engineering and design, 2000, 197(1-2): 197-203.
[63] Wang J., Gao J.X., Guo W.L., et al. Effects of specimen thickness, hardening and crack closure for the plastic strip model[J]. Theoretical and applied fracture mechanics, 1998, 29: 49-57.
[64] Jen Y.,Chang L. Effects of thickness of face sheet on the bending fatigue strength of aluminum honeycomb sandwich beams[J]. Engineering Fracture Mechanics, 2009, 16: 1282-1293.
[65] Shipilov S.A. Effects of stress ratio on the mechanism of environmentally-assisted fatigue crack growth in high strength steels[J]. Strenght of materials, 1995, 27(1-2): 64-69.
[66] Chang T., Li G., Hou J. Effects of applied stress level on plastic zone size and opening stress ratio of a fatigue crack[J]. International journal of fatigue, 2005, 27: 519-526.
[67] Newman J.C., Ruschau J.J. The stress level effect on fatigue crack growth under constant amplitude loading[J]. International journal of fatigue, 2007, 29: 1608-1615.
[68] Runt J., Gallagher K.P. The influence of microstructure on fatigue crack propagation inpolyoxymethylene[J]. Journal of materials science, 1991, 26: 792-798.
[69] Fonte M.A., Stanzl-Tschegg S.E., Holper B., et al. The microstructure and enviroments influence on fatigue crack growth in 7049 aluminum alloy at different load ratios[J]. International journal of fatigue, 2001, 23: S311-S317.
[70] Saengsai A., Miyashita Y., Mutoh Y. Effects of humidity and contact material on fretting behavior of an extruded AZ61 magnesium alloy[J]. Tribology international, 2009, 42(9): 1346-1351.
[71]傅惠民,高镇同. a-N(a-t)曲线三参数米函数拟合法[J].航空学报, 1989, 10(12): B666-B670.
[72]傅惠民,高镇同.给定寿命下的疲劳裂纹尺寸分布[J].航空学报, 1988, 9(3): A113-A118.
[73]田秀云,孙智强. 2024-T2铝合金疲劳裂纹扩展曲线的拟合方法研究[J].航空学报, 2003, 24(2): 144-146.
[74]王红军,徐人平.常用a-N曲线拟合方法的比较[J].机械, 2009, 36(2): 24-25.
[75] Erdogan F., Sih G.C. On the extension in plates under plane loading and transverse shear[J]. Journal of Basic Engineering, 1963: 519-527.
[76]牟宗花,杜善义,张泽华.拉压强度不同材料的复合型断裂准则[J].哈尔滨工业大学学报, 1995, 27(6): 38-41.
[77] Skelton R.P., Vilhelmsen T., Webster G.A. Energy criteria and cumulative damage during fatigue crack growth[J]. International journal of fatigue, 1998, 20(9): 641-649.
[78]刘小妹,刘一华,梁拥成等.复合型V形切口脆断的应变能密度因子准则[J].机械强度, 2008, 30(2): 288-292.
[79]淳庆.应力强度因子和裂纹扩展判据的典型算法[J].江苏大学学报(自然科学版), 2011, 32(3): 354-358.
[80] Melenk J.M., Babuska I. the partition of unity finite element method: basic theory and applications[J]. Computer methods in applied mechanics and engineering, 1996, 139: 289-314.
[81] Belytschko T., Black T. Elastic crack growth in finite elements with minimal remeshing[J]. International journal for numerical methods in engineering, 1999, 45: 601-620.
[82] Moes N., Dolbow J., Belytschko T. A finite element method for crack growth without remeshing[J]. International journal for numerical methods in engineering, 1999, 46: 131-150.
[83] Dolbow J., Moes N., Belytschko T. Discontinuous enrichment in finite elements with a partition of unity method[J]. Finite elements in analysis and design, 2000, 36: 235-260.
[84] Daux C., Moes N., Dolbow J.,et al. Arbitrary branched and intersecting cracks with theextended finite element method[J]. International journal for numerical methods in engineering, 2000, 48: 1741-1760.
[85] Belytschko T., Moes N., Usui S., et al. Arbitrary discontinuities in finite elements[J]. International journal for numerical methods in engineering, 2001, 50: 993-1013.
[86] Sukumar N., Chopp D.L., Moes N.,et al. Modelling holes and inclusions by level sets in the extended finite element method[J]. Computer methods in applied mechanics and engineering, 2001, 190: 6183-6200.
[87] Belytschko T., Gracie R., Ventura G. A review of extended/generalized finite element methods for material modeling[J]. Modeling and simulation in materials science and engineering, 2009, 17: 1-24.
[88] Bechet E., Minnebo H., Moes N., et al. Improved implementation and robustness study of the X-FEM for stres analysis around cracks[J]. International journal for numerical methods in engineering, 2005, 64: 1033-1056.
[89] Laborde P., Pommier J., Renard Y., et al. High order extended finite element method for cracked domains[J]. International journal for numerical methods in engineering, 2005, 64: 354-381.
[90] Xiao Q.Z., Karihaloo B.L. Improving the accuracy of XFEM crack tip field using higher order quadrature and statically admissible stress recovery[J]. International journal for numerical methods in engineering, 2006, 66(9): 1378-1410.
[91] Liu X.Y., Xiao Q.Z., Karihaloo B.L. XFEM for direct evaluation of mixed mode SIFs in homogeneous and bi-materials[J]. International journal for numerical methods in engineering, 2004, 59: 1103-1118.
[92] Xiao Q.Z., Karihaloo B.L., Liu X.Y. Incremental-secant modulus iteration scheme and stress recovery for simulating cracking process in quasi-brittle materials using XFEM[J]. International journal for numerical methods in engineering, 2007, 69: 2606-2635.
[93] Wyart E., Coulon D., Duflot M., et al. A substructured FE-shell/XFEM-3D method for crack analysis in thin-walled structures[J]. International journal for numerical methods in engineering, 2007, 72: 757-779.
[94] Osher S., Sethian J.A. Front propagating with curvature dependent speed: algorithms based on Hamilton-Jacobi formulations[J]. Journal of computational physics, 1988, 79: 12-49.
[95] Sethian J.A. Level set methods and fast marching methods: Evolving interfaces in computational geometry, fluid mechanics[M]. Cambridge Cambridge university press, 1999.
[96] Stolarska M., Chopp D.L., Moes N., et al. Modelling crack growth by level sets in the extendedfinite element method[J]. International journal for numerical methods in engineering, 2001, 51: 943-960.
[97] Moes N., Gravouil A., Belytschko T. Non-planar 3D crack growth by the extended finite element and level sets-part I mechanical model[J]. International journal for numerical methods in engineering, 2002, 53(11): 2549-2568.
[98] Chopp D.L., Sukumar N. Fatigue crack propagation of multiple coplanar cracks with the coupled extended finite element and fast marching method[J]. International journal of engineering science, 2003, 41(8): 845-869.
[99]方修君,金峰.基于ABAQUS平台的扩展有限元法[J].工程力学, 2007, 24(7): 6-10.
[100] Shi J., Chopp D., Lua J., et al. Abaqus implementation of extended finite element method using a level set respresentation for three dimensional fatigue crack growth and life predictions[J]. Engineering Fracture Mechanics, 2010, 77: 2840-2863.
[101]李录贤,王铁军.扩展有限元法(XFEM)及其应用[J].力学进展, 2005, 35(1): 5-20.
[102]余天堂.含裂纹体的数值模拟[J].岩石力学与工程学报, 2005, 24(24): 4434-4439.
[103]余天堂.扩展有限元法的数值方面[J].岩土力学, 2007, 28(增刊): 305-310.
[104]董玉文,余天堂,任青文.直接计算应力强度因子的扩展有限元法[J].计算力学学报, 2008, 25(1): 72-77.
[105]喻葭临,张其光,于玉贞等.扩展有限元中非连续区域的一种积分方案[J].清华大学学报(自然科学版), 2009, 49(3): 351-354.
[106]刘波波.基于时域精细算法与扩展有限元技术的粘弹性位移场分析[D].大连:大连理工大学, 2009.
[107]朱传锐.基于扩展有限元和水平集理论的裂纹扩展问题研究[D].焦作:河南理工大学, 2010.
[108]陈连玉,周东清,郭锦华.国外引进软件二次开发的若干技术问题[J].大连理工大学学报, 1999, 39(5): 706-709.
[109]谢配良,薛海,盛伟. ANSYS软件的二次开发及其在大容量缓冲器模锻件上的应用[J].微机应用, 2000, 6: 26-28.
[110]齐慧,杨屹,蒋玉明.基于ANSYS软件二次开发的铸造充型和凝固耦合过程数值模拟研究[J].四川大学学报(工程科学版), 2001, 33(5): 47-50.
[111]陈文.基于灵敏度与模拟退火方法的模型修正及软件二次开发[D].南京:南京航空航天大学, 2008.
[112]徐飞英. ADINA软件二次开发初探[J].江西化工, 2008, 1: 138-140.
[113]曹琳,赵继伟. ADINA软件的二次开发[J].人民黄河, 2009, 31(7): 96-97.
[114]李健,杨坤.基于ABAQUS软件二次开发技术筒形件旋压过程研究[J].锻压技术, 2009, 34(6): 129-132.
[115]刘建涛,杜平安,黄明镜等.曲面薄壳有限元离散误差分析和修正方法研究[J].系统仿真学报, 2010, 22(10):2281-2286.
[116]刘长福,邓明.航空发动机结构分析[M].西安:西北工业大学出版社, 2005.
[117] You J.F., Chen R.X. Buckling analysis on rear dome of solid rocket motor case[J]. Journal of Solid Rocket Technology, 2008, 31(2): 173-178.
[118]懂永辉,况雨春,伍开松等.弯曲井眼中钻柱屈曲的非线性有限元分析[J].石油机械, 2008, 36(4): 25-27.
[119]任建峰,仇原鹰,段宝岩等.一种基础加速度冲击的仿真新方法[J].现代机械, 2006, 2: 21-23.
[120] Chopra A.K. (著),谢礼立,吕大刚(译).结构动力学理论及其在地震工程中的应用[M].北京:高等教育出版社, 2005.
[121]管德清.焊接钢结构疲劳强度与寿命预测理论的研究[D].长沙:湖南大学, 2003.
[122] Lee Y.L., Pan J., Hathaway R.B., et al. Fatigue testing and analysis (Theory and practice)[M]. Burlington: Elsevier Butterworth-Heinemann, 2005.
[123]赵建生.断裂力学及断裂物理[M].武昌:华中科技大学出版社, 2006.
[124]董慧茹,郭万林.复合型裂纹起裂角厚度效应的实验研究[J].工程力学, 2004, 21(4):123-127.
[125] Zhao T.W., Zhang J.X., Jiang Y.Y. A study of fatigue crack growth of 7075-T651 aluminum alloy[J]. International journal of fatigue, 2008, 30: 1169-1180.
[126] Ray A., Patankar R. Fatigue crack growth under variable-amplitude loading: part I-model formulation in state space setting[J]. Applied mathematical modeling, 2001, 25: 979-994.
[127] Lee E.U., Vasudevan A.K., Sadananda K. Effects of various environments on fatigue crack growth in Laser formed and IM Ti-6Al-4V alloys[J]. International journal of fatigue, 2005, 27: 1597-1607.
[128]高艳丽. 16Mn钢焊接件疲劳裂纹萌生与扩展的研究[D].沈阳:沈阳大学, 2007.
[129] Newman J.C. A crack opening stress equation for fatigue crack growth[J]. International journal of fracture, 1984, 24: R131-R135.
[130] Huang X.P., Han Y., Cui W.C., et al. Fatigue life prediction of weld-joints under variable amplitude fatigue loads[J]. Journal of ship mechanics, 2005, 9(1): 89-97.
[131] Codrington J., Kotousov A. A crack closure model of fatigue crack growth in plates of finite thickness under small scale yielding conditions[J]. Mechanics of materials, 2009, 41: 165-173.
[132] Hsu K., Lin C. Effects of R ratio on high temperature fatigue crack growth behavior of a precipitation-hardening stainless steel[J]. International journal of fatigue, 2008, 30: 2147-2155.
[133] Paris P.C., Tada H., Donald J.K. Service load fatigue damage——a historical perspective[J]. International journal of fatigue, 1999, 21: S35-S46.
[134] Voorwald H.J.C., Torres M.A.S., Junior C.C.E.P. Modeling of fatigue crack growth following overloads[J]. International journal of fatigue, 1991, 13: 423-427.
[135] Liu J.T., Du P.A., Huang M.J., et al. New model of propagation rates of long crack due to structure fatigue[J]. Applied mathematics and mechanics, 2009, 30(5): 575-584.
[136] Chang T., Guo W. A model for the through-thickness fatigue crack closure[J]. Engineering Fracture Mechanics, 1999, 64: 59-65.
[137] Porter T.R. Method of analysis and prediction for variable amplitude fatigue crack growth[J]. Engineering Fracture Mechanics, 1972, 4: 717-736.
[138] Yisheng W., Schijve J. Fatigue crack closure measurements on 2024-T3 sheet specimens[J]. Fatigue & Fracture of engineering materials & structures, 1995, 18(9): 917-921.
[139] Comi C., Mariani S. Extended finite lement simulation of quasi-brittle fracture in functionally graded materials[J]. Computer methods in applied mechanics and engineering, 2007, 196: 4013-4026.
[140]方修君,金峰,王进廷.基于扩展有限元法的Koyna重力坝地震开裂过程模拟[J].清华大学学报(自然科学版), 2008, 48(12): 2065-2069.
[141] Pais M. J. Accurate integration of fatigue crack growth models through kriging and reanalysis of the extended finite elemtn method[D]. Gainesville: University of Florida, 2010.
[142] Babuska I., Zhang Z.M. The partition of unity method for the elastically supported beam[J]. Computer methods in applied mechanics and engineering, 1998, 152(1-2): 1-18.
[143] Williams M. On the stress distribution at the base of a stationary crack[J]. Journal of applied mechanics, 1957, 24(1): 109-114.
[144]中国航空研究院.应力强度因子手册(增订版) [M].北京:科学出版社, 1993.
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